Robert M. Jones

Crushing Characteristics of Continuous Fiber-Reinforced Composite Tubes

Composite tubes can be reinforced with continuous fibers. When such tubes are subjected to crushing loads, the response is complex and depends on interaction between the different mechanisms that control the crushing process. The modes of crush ing and their controlling mechanisms are described. Also, the resulting crushing process and its efficiency are addressed.

Stress-strain relations for materials with different moduli in tension and compression

Models in the form of stress-strain, or constitutive, relations are discussed for materials with moduli under tensile loading which are different from those under compressive loading. Criteria for consistent material models are given which are based on the principles of anisotropic elasticity and on the known behavior of such materials. The Ambartsumyan material model is compared with the criteria and found to violate the requirement of symmetric compliances. An improved model, called the weighted compliance matrix (WCM) material model, is shown to satisfy the criteria for isotropic and orthotropic bodies under plane stress. The new model can be extended by deduction to more complicated situations such as anisotropic bodies under general stress states.

Buckling and Vibration of Unsymmetrically Laminated Cross-Ply Rectangular Plates

An exact solution and numerical results are presented for simply supported plates that are laminated unsymmetrically about their middle surface. The coupling between bending and extension induced by the lamination asymmetry substantially decreases buckling loads and vibration frequencies for common composite materials such as boron/epoxy and graphite/epoxy. For antisymmetric laminates, the effect of the coupling dies out rapidly as the number of layers is increased. For generally unsymmetric laminates, however, the effect of coupling dies out very slowly as the number of layers increases. That is, having a large number of layers is no guarantee that coupling will not seriously degrade buckling resistance and vibration frequencies. Thus, designers must include coupling between bending and extension in all analyses of unsymmetrically laminated plates.

Prediction of the Energy-Absorption Capability of Composite Tubes

A method of predicting the crash-related energy-absorption capability of composite tubes is presented. The method is based upon a phenomenological model of the crushing process exhibited by continuous-fiber-reinforced tubes. A finite element method is used to model the crushing process. The analysis is compared with experiments on Kevlar-epoxy and graphite-epoxy tubes. Reasonable agreement is obtained between the analysis and experiment.

Analogy for the effect of material and geometrical variables on energy-absorption capability of composite tubes

Simplified procedures for determining the qualitative effect a variable has on structural response of a composite tube are very useful in both preliminary design as well as in providing insight into the general response. An analysis procedure is pre sented that can be used to determine the qualitative change in the sustained crushing load due to a change in specimen material properties or geometry. The analysis procedure is similar in form to the equation for the buckling load of a column on an elastic foun dation.

BUCKLING OF CIRCULAR CYLINDRICAL SHELLS WITH MULTIPLE ORTHOTROPIC LAYERS AND ECCENTRIC STIFFENERS

An exact solution is derived for the buckling of a circular cylindrical shell with multiple orthotropic layers and eccentric stiffeners under axial compression, lateral pressure, or any combination thereof. Classical stability theory (membrane prebuckled shape) is used for simply supported edge boundary conditions. The present theory enables the study of coupling between bending and extension due to the presence of different layers in the shell and the presence of eccentric stiffeners. Previous approaches to stiffened multilayered shells are shown to be erratic in the prediction of buckling results because of neglect of coupling between bending and extension.

Crushing characteristics of composite tubes with near-elliptical' cross sections

An experimental investigation was conducted to determine whether the energy-absorption capability of near-elliptical cross-section composite tubular specimens is a function of included angle. Each half of the near-elliptical cross-section tube is a seg ment of a circle. The included angle is the angle created by radial lines extending from the center of the circular segment to the ends of the circular segment. Graphite- and Kevlar- reinforced epoxy material was used to fabricate specimens. Tube ply orientation was [±45] N where the number of ±45 pairs was 2, 4, 6, and 12. Tube internal diameters were 2.54, 3.81, and 7.62 cm, and included angles were 180, 160, 135, 115, and 90 degrees. Based upon the test results from these tubes, energy-absorption capability increased between 10 and 30 percent as included angle decreased between 180 and 90 degrees for the materials evaluated. Energy-absorption capability was a decreasing nonlinear function of the ratio of tube internal diameter to wall thickness.

Apparent Flexural Modulus and Strength of Multimodulus Materials

The ASTM flexure test is commonly used to measure the flexural modulus and flexural strength of materials other than the plastics for which it was originally developed. The officially designated equations for reporting the test results are applicable only to materials that are linear elastic to failure. However, the test is often used for carbon-carbon and other composite materials which have different (and sometimes nonlinear) stress-strain curves under tension loading than under compression loading. Such materials are called multimodulus materials. The influence of the multimodulus characteristic on the behavior of a test beam is evaluated for two representative carbon-carbon composite materials. The ASTM flexure test is found to be inapplicable to this class of materials because of the multimodulus characteristic and the nonlinear stress-strain behavior.

Bending and extension of cross-ply laminates with different moduli in tension and compression

Abstract Composite materials often exhibit different stiffnesses or moduli under tension loading than under compression loading. This behavior is modeled with a bilinear stress-strain curve having a modulus E t in tension and E c in compression as an approximation to the real nonlinear behavior. Under bending loads, laminated composites have both tensile and compressive stresses and hence are not subject to the same behavioral rules as ordinary single modulus materials. The resulting transcendental equilibrium equation is dependent upon the unknown neutral surface. This neutral surface is found and, hence, the equilibrium problem is solved with an iteration technique. The approach is applied to laminates ordinarily thought to be symmetric, antisymmetric, and unsymmetric about the middle surface. All laminates are found to exhibit coupling between bending and extension under bending in contrast to the usual concepts of symmetry and antisymmetry for single modulus laminates. Several approximate approaches are investigated for treating the multimodulus laminate problem. The effect of coupling due to different moduli in tension and compression on stresses and deflections is found to be generally significant for common composite materials such as boron/epoxy and graphitc/epoxy as well as carbon-carbon.

A New Material Model for the Nonlinear Biaxial Behavior of ATJ-S Graphite*

A new model for the deformation behavior of ATJ-S graphite, a non linear transversely isotropic material, under initial loading is described. This material model, which is based on a new deformation theory of ortho tropic plasticity, has excellent potential for description of the biaxial softening phenomenon found in ATJ-S graphite. Biaxial softening is char acterized by the development of larger strains in biaxial tension than in uniaxial tension, in contradiction to conventional Poisson effects. The new model is examined for sensitivity to (1) a nonsymmetric compliance matrix, (2) how the material model constants are obtained, and (3) varia tions in material properties. Comparisons are made between strain values obtained with the material model incorporated in a finite element com puter analysis and strain values from biaxial test results.